Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups

We consider noncommutative GUT inspired field theories formulated within the enveloping-algebra formalism for anomaly safe compact simple gauge groups. Our theories have only gauge fields and fermions, and we compute the UV divergent part of the one-loop background-field effective action involving two fermionic fields at first order in the noncommutativity parameter theta. We show that, if the second-degree Casimir has the same value for all the irreps furnished by the fermionic multiplets of the model, then, that UV divergent part can be renormalised by carrying out multiplicative renormalisations of the coupling constant, theta and the fields, along with the inclusion of theta-dependent counterterms which vanish upon imposing the equations of motion. These theta-dependent counterterms have no physical effect since they vanish on-shell. This result along with the vanishing of the UV divergent part of the fermionic four-point functions leads to the unexpected conclusion that the one-loop matter sector of the background-field effective action of these theories is one-loop multiplicatively renormalisable on-shell. We also show that the background-field effective action of the gauge sector of the theories considered here receives no theta-dependent UV divergent contributions at one-loop. We thus conclude that these theories are on-shell one-loop multiplicatively renormalisable at first order in theta.Comment: 20 pages, 3 figure

Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences

Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a \theta-deformed nonlinear realisation of the {\cal N}=1 supersymmetry algebra in four dimensions. For the latter theory we work out at one-loop and first order in the noncommutative parameter matrix \theta^{\mu\nu} the UV divergent part of its effective action in the background-field gauge, and, for N>=2, we show that for finite values of N the gauge sector fails to be renormalisable; however, in the large N limit the full theory is renormalisable, in keeping with the expectations raised by the quantum behaviour of the theory's noncommutative classical dual. We also obtain --for N>=3, the case with N=2 being trivial-- the UV divergent part of the effective action of the SU(N) noncommutative theory in the enveloping-algebra formalism that is obtained from the previous ordinary U(N) theory by removing the U(1) degrees of freedom. This noncommutative SU(N) theory is also renormalisable.Comment: 33 pages, 4 figures. Version 2: Unnecessary files removed. Version 3: New types of field redefinitions were considered, which make the large N U(N) and the SU(N) theories renormalisable. The conclusions for U(N) with finite N remain unchanged. Version 4: Corrected mistyped equations, minor revision

Quantization of a gauge theory on a curved noncommutative space

We study quantization of a gauge analogon of the Grosse-Wulkenhaar model: we find divergent one-loop contributions to the 1-point and 2-point Green functions. We obtain that five counterterms are necessary for renormalization and that all divergences are logarithmic.Comment: 23 pages, 3 figure

A Dynamical 2-dimensional Fuzzy Space

The noncommutative extension of a dynamical 2-dimensional space-time is given and some of its properties discussed. Wick rotation to euclidean signature yields a surface which has as commutative limit the doughnut but in a singular limit in which the radius of the hole tends to zero.Comment: 13 pages, accepted for publication in Phys. Lett.

Renormalizability of noncommutative SU(N) gauge theory

We analyze the renormalizability properties of pure gauge noncommutative SU(N) theory in the $\theta$-expanded approach. We find that the theory is one-loop renormalizable to first order in $\theta$.Comment: 11 pages, minor changes, accepted for publication in JHE

Hidden parameters in open-system evolution unveiled by geometric phase

We find a class of open-system models in which individual quantum trajectories may depend on parameters that are undetermined by the full open-system evolution. This dependence is imprinted in the geometric phase associated with such trajectories and persists after averaging. Our findings indicate a potential source of ambiguity in the quantum trajectory approach to open quantum systems.Comment: QSD analysis added; several stylistic changes; journal reference adde

Spherically Symmetric Noncommutative Space: d = 4

In order to find a noncommutative analog of Schwarzschild or Schhwarzschild-de Sitter blackhole we investigate spherically symmetric spaces generated by four noncommutative coordinates in the frame formalism. We present two solutions which however do not posess the prescribed commutative limit. Our analysis indicates that the appropriate noncommutative space might be found as a subspace of a higher-dimensional space.Comment: 14 page

Genetika i arheologija - mogućnosti interdisciplinarnog povezivanja

Rad u prvom dijelu donosi osnovne pojmove o DNA molekuli, a u drugom o njenim mogućnostima u arheologiji uz primjere dosadašnje primjene u svijetu. Također su prikazani glavni problemi samog očuvanja potencijalnog materijala i metodologije njegova izoliranja

Emergence of classical behavior from the quantum spin

Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum states into equivalence classes, and forces the equivalence classes to evolve as single units representing the classical states. The coarse-grained quantum spin with the constrained evolution in the limit of the large spin becomes indistinguishable from the classical system

TeV Scale Implications of Non Commutative Space time in Laboratory Frame with Polarized Beams

We analyze $e^{+}e^{-}\rightarrow \gamma\gamma$, $e^{-}\gamma \rightarrow e^{-}\gamma$ and $\gamma\gamma \rightarrow e^{+}e^{-}$ processes within the Seiberg-Witten expanded noncommutative scenario using polarized beams. With unpolarized beams the leading order effects of non commutativity starts from second order in non commutative(NC) parameter i.e. $O(\Theta^2)$, while with polarized beams these corrections appear at first order ($O(\Theta)$) in cross section. The corrections in Compton case can probe the magnetic component($\vec{\Theta}_B$) while in Pair production and Pair annihilation probe the electric component($\vec{\Theta}_E$) of NC parameter. We include the effects of earth rotation in our analysis. This study is done by investigating the effects of non commutativity on different time averaged cross section observables. The results which also depends on the position of the collider, can provide clear and distinct signatures of the model testable at the International Linear Collider(ILC).Comment: 22 pages, 19 figures, new comments and references added, few typos corrected, Published in JHE